Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest, catches and releases of rockfish in Alaska waters. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and thus does not rely on the decision tree approach in the original Howard methods. Furthermore, the Bayesian approach should provide sport fish harvest, catch and mortality estimates back to 1978 when the SWHS was implemented. Harvest estimates should be mostly consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data. Furthermore, the Howard methods are wholly reliant on logbook release estimates and ignore the release estimates from the SWHS data (inferred from the catch and harvest estimates). Here we explore several models that attempt to balance all of the data in estimating releases.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are estimates from 1977- 1995 that required some partitioning work to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied.

**Figure 0.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook harvests are a census of guided harvests.

Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides were required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 1.**- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).

Figure 1.- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).


The Howard methods treat the logbook release data as a census and then use the ratio of guided:unguided releases in the SWHS to expand the logbook release estimates to generate total and unguided estimates.

To evaluate this discrepancy, several models were used to estimate releases in this exploration. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treats the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development to date has revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish.

A current challenge at this juncture is how to accommodate the prohibition on retaining yelloweye in Southeast from 2020 through 2024. Because it is closed to retention the port sampling data is not reflective of releases while remaining an accurate description of the harvest. Current modelling efforts revolve around developing a separate yelloweye curve that censors the missing data.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta1_{(comp)ayu} + \frac{\beta2_{(comp)ayu}}{(1 + exp(\beta3_{(comp)ayu}*(y - \beta4_{(comp)ayu})))} + \beta5_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested by area, year, user group and species grouping , \(pH_{(comp)ayu}\). Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta1_{(pH)ayu} + \frac{\beta2_{(pH)ayuc}}{(1 + exp(\beta3_{(pH)ayuc}*(y - \beta4_{(pH)ayuc})))} + \beta5_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), several approaches have been explored. In the first approach model \(LB_{fit}\) treats the release data as a true census and the releases are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Similar to how harvests were modeled, central and Kodiak \(R_{(nonpel,nonye)ay1}\) was equal to total releases minus pelagic and yelloweye releases while for southeast areas it was equal to the sum of DSR and slope releases minues yelloweye releases.

In the second approach we consider the logbook release data to be a minimal estimate of the true releases. Thus model \(LB_{cens}\) censors the release data (censored data is entered as NA) and treats the reported releases as a minimal number such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(ye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(ye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(ye)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(nonpel,nonye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(nonpel,nonye)ay}, \infty\right) \end{equation}\]

Model \(LB_{hyb}\) is a hybrid approach that treats the yelloweye releases as a reliable census of yelloweye releases (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled differently in the \(LB_{fit}\), \(LB_{cens}\), and \(LB_{hyb}\) models. Because the \(LB_{fit}\) model assumes that logbook release data is true and the poison likelihoods assume a much smaller variance than the large variances associated with the SWHS release estimates, SWHS release estimates \(b_R{ay}\) were modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The \(LB_{cens}\) model treats the logbook release data as lower bound on the release estimates and thus the likelihood linking true releases to the SWHS release estimates is dominant. During model development it was apparent that estimating bias in the SWHS data was more difficult and a different structure was employed that assumed bias in SWHS release data followed a similar pattern to that of the harvests but is offset by some area specific amount. In these models \(b_R{ay}\) differed from \(b_H{ay}\) by offset \(Rboff_{a}\) such that

\[\begin{equation} b_R{ay}~=~b_H{ay} + Rboff_{ay} \end{equation}\]

where

\[\begin{equation} Rboff_{a}~\sim~\textrm{Normal}(\mu_{(bR)r}, \sigma_{(bR)r}) \end{equation}\]

such that \(Rboff_{a}\) was modeled hierarchically across region r.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs and the number of yellow rockfish sampled modeled analogously with an appropriately substituted \(N\).

Unresolved issues and outstanding questions:

Models detailed in this markdown represent the next step in the modelling process whereby the pH parameters are separated out by species. This approach separates the compositional data that is germaine to the harvests from the release estimates and releases are now based on pH. Additionally, this approach allows the pH parameters to differ between pelagic and yelloweye which is appropriate given regulatory changes as well as fisherman and industry behaviour and is born out in the results. The approach results in great uncertainty around unguided release estimates, but that uncertainty is appropriate given the data. These models handle the yelloweye closures in southeast much more appropriately given that the compositional data is no longer directly applied to the release estimates. These versions of the model are in development and it is unclear whether the \(LB_{cens}\) model would work, but it appears applicable to the \(LB_{fit}\) and \(LB_{hyb}\) approaches.

Other issues include:

  1. Complete convergence has not been achieved and the logistic curve parameters for p_pelagic and p_yellow remain the last sticking point. I think that p_pelagic will resolve with longer chains.
  2. Estimate precision: These models are producing more precise harvest estimates that in Adam’s original model. I am not sure why at this juncture. sigma_H on the spline was switched from a fixed value to a prior centered around that fixed value, but the model estimates are in the same range as the fixed value. Would the number of knots in the spline explain this? 7 knots was settled on during early model fitting when it clearly performed better than fewer or more knots.
  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.
  4. Random effects on pH: These are currently used in the model but because pH isn’t linked to data as the p_comp data is I am not sure what to make of them or if they are appropriate.
  5. Model comparisons: I need to write code for comparing models side by side as well as quantifying the differences between these methods and the Howard methods.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 2.**- Total rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- DSR rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- DSR rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- DSR rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- DSR rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Slope rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Slope rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

**Figure 8.**- Residuals from logbook harvests

Figure 8.- Residuals from logbook harvests


SWHS residuals

**Figure 9.**- Residuals from SWHS harvests.

Figure 9.- Residuals from SWHS harvests.



**Figure 10.**- Residual of SWHS releases

Figure 10.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 11.**- Mean percent of harvest by charter anglers.

Figure 11.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 12.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 12.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 13.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 13.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.


**Figure 13.**- Annual proportion of DSR rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

Figure 13.- Annual proportion of DSR rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.


**Figure 13.**- Annual proportion of Slope rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

Figure 13.- Annual proportion of Slope rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

SWHS bias

Figure 14 shows the mean estimate for SWHS bias. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias.

**Figure 14.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 14.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS bias track observations fairly well when he have guided harvest estimates. There are some disturbing trends/patterns seen in the earlier time periods. Often the patterns represent periods where SWHS estimates and guide logbook estimates do not follow the recent relationship. I’m not sure what drives the trends but it seems plausible to me that long-term changes in the ratio of charter and private anglers may be a factor. If Charter/Private ratio information is available in the historical creel data it my be helpful here (particularly for North Southeast Inside and South Southeast outside).

**Figure 15.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 15.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 8 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 16.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 16.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment.

**Figure 17.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 17.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta0_pH 23 2.918604
mu_beta0_pH 3 2.520940
beta3_pH 20 2.240394
beta1_pH 27 1.919914
beta3_black 2 1.828106
beta0_black 2 1.735659
beta1_black 10 1.630202
beta_H 5 1.558067
beta2_pelagic 2 1.453473
beta2_pH 18 1.407730
beta2_yellow 2 1.306545
beta3_pelagic 2 1.302669
parameter n badRhat_avg
beta2_black 2 1.302297
tau_beta0_pH 4 1.294405
beta0_yellow 2 1.243939
mu_bc_H 1 1.219715
beta1_pelagic 6 1.211312
beta1_yellow 3 1.189265
beta3_yellow 3 1.174554
beta4_pelagic 2 1.144763
tau_beta0_pelagic 1 1.135976
sd_comp 1 1.133027
beta0_pelagic 3 1.129889
Table 2. Summary of unconverged parameters by area
afognak BSAI CI CSEO eastside EWYKT NG northeast NSEI NSEO PWSI PWSO SOKO2SAP SSEI SSEO WKMA
beta_H 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
beta0_black 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0
beta0_pelagic 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0
beta0_pH 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1
beta0_yellow 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1
beta1_black 1 1 1 0 1 0 1 1 0 0 1 1 0 1 1 0
beta1_pelagic 1 0 1 1 1 0 0 0 0 0 0 1 0 0 0 1
beta1_pH 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1
beta1_yellow 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1
beta2_black 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0
beta2_pelagic 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0
beta2_pH 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1
beta2_yellow 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0
beta3_black 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0
beta3_pelagic 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0
beta3_pH 0 0 1 1 1 1 0 0 1 1 1 1 0 1 1 0
beta3_yellow 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1
beta4_pelagic 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0
mu_bc_H 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
mu_beta0_pH 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0
sd_comp 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta0_pelagic 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta0_pH 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.135 0.070 -0.262 -0.138 0.010
mu_bc_H[2] -0.097 0.045 -0.175 -0.100 0.000
mu_bc_H[3] -0.433 0.071 -0.566 -0.435 -0.295
mu_bc_H[4] -0.986 0.195 -1.395 -0.982 -0.609
mu_bc_H[5] 0.851 0.868 -0.173 0.708 2.884
mu_bc_H[6] -2.218 0.317 -2.815 -2.227 -1.594
mu_bc_H[7] -0.464 0.110 -0.689 -0.460 -0.248
mu_bc_H[8] 0.241 0.361 -0.361 0.206 1.052
mu_bc_H[9] -0.307 0.136 -0.575 -0.306 -0.043
mu_bc_H[10] -0.113 0.070 -0.244 -0.113 0.029
mu_bc_H[11] -0.106 0.041 -0.185 -0.106 -0.022
mu_bc_H[12] -0.250 0.105 -0.479 -0.245 -0.055
mu_bc_H[13] -0.117 0.081 -0.272 -0.120 0.048
mu_bc_H[14] -0.280 0.094 -0.465 -0.277 -0.105
mu_bc_H[15] -0.343 0.054 -0.444 -0.345 -0.234
mu_bc_H[16] -0.281 0.432 -1.012 -0.314 0.615
mu_bc_R[1] 1.349 0.140 1.079 1.347 1.622
mu_bc_R[2] 1.490 0.090 1.308 1.491 1.662
mu_bc_R[3] 1.442 0.141 1.165 1.445 1.709
mu_bc_R[4] 0.984 0.198 0.565 0.993 1.347
mu_bc_R[5] 1.172 0.452 0.263 1.180 2.039
mu_bc_R[6] -1.529 0.421 -2.388 -1.523 -0.712
mu_bc_R[7] 0.280 0.194 -0.110 0.283 0.656
mu_bc_R[8] 0.539 0.195 0.137 0.538 0.910
mu_bc_R[9] 0.372 0.199 -0.035 0.382 0.735
mu_bc_R[10] 1.320 0.132 1.042 1.325 1.566
mu_bc_R[11] 1.129 0.074 0.983 1.129 1.274
mu_bc_R[12] 0.925 0.192 0.542 0.929 1.309
mu_bc_R[13] 1.044 0.100 0.844 1.044 1.240
mu_bc_R[14] 0.970 0.145 0.695 0.971 1.257
mu_bc_R[15] 0.877 0.095 0.696 0.878 1.065
mu_bc_R[16] 1.195 0.132 0.928 1.195 1.451
tau_pH[1] 2.838 0.278 2.319 2.827 3.415
tau_pH[2] 2.207 0.981 0.757 2.626 3.530
tau_pH[3] 2.897 0.418 2.123 2.876 3.763
tau_pH[4] 9.318 2.235 5.641 9.129 14.019
tau_pH[5] 5.262 1.601 2.673 5.076 8.928
beta0_pH[1,1] 0.549 0.239 0.029 0.564 0.976
beta0_pH[2,1] 1.326 0.230 0.867 1.329 1.761
beta0_pH[3,1] 1.322 0.278 0.696 1.338 1.794
beta0_pH[4,1] 1.654 0.276 1.083 1.668 2.163
beta0_pH[5,1] -0.431 0.505 -1.258 -0.489 0.916
beta0_pH[6,1] 0.179 0.538 -0.934 0.228 1.050
beta0_pH[7,1] 0.375 0.511 -0.689 0.582 1.008
beta0_pH[8,1] -0.506 0.301 -1.135 -0.481 -0.014
beta0_pH[9,1] -0.449 0.276 -0.997 -0.444 0.070
beta0_pH[10,1] 0.387 0.254 -0.109 0.385 0.878
beta0_pH[11,1] -0.261 0.281 -0.886 -0.242 0.235
beta0_pH[12,1] 0.565 0.246 0.056 0.574 1.025
beta0_pH[13,1] 0.142 0.342 -0.456 0.121 0.839
beta0_pH[14,1] -0.155 0.593 -0.975 -0.308 1.341
beta0_pH[15,1] 0.197 0.666 -0.983 0.182 1.471
beta0_pH[16,1] 1.643 1.009 -0.762 2.061 2.593
beta0_pH[1,2] 2.679 0.269 2.151 2.696 3.170
beta0_pH[2,2] 2.872 0.273 2.235 2.903 3.276
beta0_pH[3,2] 2.581 0.409 1.840 2.531 3.372
beta0_pH[4,2] 2.593 0.336 1.858 2.659 3.131
beta0_pH[5,2] 4.682 1.608 2.425 4.378 8.533
beta0_pH[6,2] 2.957 0.344 2.342 2.954 3.642
beta0_pH[7,2] 1.928 0.251 1.458 1.932 2.406
beta0_pH[8,2] 2.811 0.271 2.346 2.823 3.258
beta0_pH[9,2] 3.027 0.675 1.622 3.218 4.034
beta0_pH[10,2] 3.731 0.267 3.173 3.731 4.265
beta0_pH[11,2] -4.919 0.368 -5.598 -4.935 -4.108
beta0_pH[12,2] -4.858 0.544 -6.060 -4.841 -3.853
beta0_pH[13,2] -4.597 0.482 -5.542 -4.605 -3.624
beta0_pH[14,2] -5.611 0.547 -6.717 -5.602 -4.552
beta0_pH[15,2] -4.163 0.410 -5.033 -4.150 -3.388
beta0_pH[16,2] -4.491 0.887 -5.603 -4.721 -2.112
beta0_pH[1,3] 1.299 0.313 0.627 1.331 1.768
beta0_pH[2,3] 2.041 0.320 1.207 2.124 2.466
beta0_pH[3,3] 2.117 0.387 1.295 2.148 2.706
beta0_pH[4,3] 2.527 0.540 1.266 2.730 3.172
beta0_pH[5,3] 0.945 2.645 -4.401 1.112 6.230
beta0_pH[6,3] -1.083 1.416 -2.566 -1.536 2.838
beta0_pH[7,3] -2.053 0.934 -3.789 -2.032 0.113
beta0_pH[8,3] 0.299 0.183 -0.064 0.299 0.665
beta0_pH[9,3] -0.050 0.332 -0.708 -0.047 0.570
beta0_pH[10,3] 0.791 0.321 0.038 0.820 1.300
beta0_pH[11,4] 0.493 1.401 -2.380 0.220 2.698
beta0_pH[12,4] 0.230 1.668 -2.456 -0.085 2.896
beta0_pH[13,4] -0.305 1.817 -3.020 -0.266 2.138
beta0_pH[14,4] 0.402 1.231 -1.341 -0.146 2.324
beta0_pH[15,4] 0.401 1.056 -0.745 -0.160 2.342
beta0_pH[16,4] 0.309 1.146 -0.918 -0.372 2.181
beta0_pH[11,5] -0.715 0.218 -1.151 -0.711 -0.296
beta0_pH[12,5] -2.296 0.623 -3.113 -2.472 -0.760
beta0_pH[13,5] -0.502 0.487 -1.626 -0.335 0.125
beta0_pH[14,5] -1.020 0.208 -1.414 -1.025 -0.588
beta0_pH[15,5] -1.143 0.189 -1.509 -1.144 -0.770
beta0_pH[16,5] -0.712 0.207 -1.130 -0.708 -0.306
beta1_pH[1,1] 3.082 0.431 2.388 3.035 4.038
beta1_pH[2,1] 2.445 0.405 1.743 2.408 3.374
beta1_pH[3,1] 2.686 0.684 1.823 2.561 4.470
beta1_pH[4,1] 3.056 0.607 2.199 2.959 4.643
beta1_pH[5,1] 1.984 0.517 0.886 1.985 3.044
beta1_pH[6,1] 2.560 0.885 1.272 2.392 4.855
beta1_pH[7,1] 1.900 1.235 0.287 1.857 3.702
beta1_pH[8,1] 3.258 0.891 2.102 3.045 5.713
beta1_pH[9,1] 2.083 0.388 1.400 2.057 2.910
beta1_pH[10,1] 2.181 0.378 1.476 2.166 2.932
beta1_pH[11,1] 6.617 0.920 5.220 6.457 8.945
beta1_pH[12,1] 2.812 0.303 2.225 2.812 3.429
beta1_pH[13,1] 5.603 1.175 3.900 5.375 8.378
beta1_pH[14,1] 14.904 5.106 8.572 13.731 28.152
beta1_pH[15,1] 7.914 1.862 4.831 7.717 11.990
beta1_pH[16,1] 12.092 4.055 6.539 11.419 23.499
beta1_pH[1,2] 4.937 20.284 0.001 0.891 42.446
beta1_pH[2,2] 2.330 4.447 0.001 0.905 14.226
beta1_pH[3,2] 25.976 117.883 0.003 1.199 491.022
beta1_pH[4,2] 3.084 9.889 0.001 0.836 19.195
beta1_pH[5,2] 2.870 18.467 0.000 0.071 14.110
beta1_pH[6,2] 1.013 2.804 0.000 0.269 3.622
beta1_pH[7,2] 0.837 3.046 0.000 0.027 6.787
beta1_pH[8,2] 0.722 2.505 0.000 0.026 5.751
beta1_pH[9,2] 0.707 1.108 0.000 0.123 2.483
beta1_pH[10,2] 6.927 18.208 0.000 0.347 71.035
beta1_pH[11,2] 6.834 0.422 5.923 6.850 7.611
beta1_pH[12,2] 6.798 0.689 5.626 6.724 8.419
beta1_pH[13,2] 7.084 0.531 6.029 7.087 8.152
beta1_pH[14,2] 7.483 0.601 6.286 7.472 8.680
beta1_pH[15,2] 6.711 0.433 5.935 6.686 7.660
beta1_pH[16,2] 6.724 1.431 3.289 7.329 8.314
beta1_pH[1,3] 1.978 0.567 1.124 1.919 3.240
beta1_pH[2,3] 0.955 1.351 0.000 0.543 5.498
beta1_pH[3,3] 5.771 23.673 0.002 0.739 104.795
beta1_pH[4,3] 2.579 24.229 0.001 0.621 8.140
beta1_pH[5,3] 6.139 13.253 1.459 3.192 31.778
beta1_pH[6,3] 5.220 9.554 1.424 3.083 24.134
beta1_pH[7,3] 2.921 0.918 1.129 2.869 4.698
beta1_pH[8,3] 2.720 0.320 2.105 2.719 3.370
beta1_pH[9,3] 2.152 0.383 1.415 2.157 2.909
beta1_pH[10,3] 2.595 0.399 1.940 2.571 3.467
beta1_pH[11,4] 2.354 1.497 0.061 2.612 5.218
beta1_pH[12,4] 2.717 1.663 0.064 2.962 5.434
beta1_pH[13,4] 2.732 1.835 0.064 2.639 5.512
beta1_pH[14,4] 2.073 1.254 0.046 2.493 4.163
beta1_pH[15,4] 1.920 1.063 0.078 2.310 3.565
beta1_pH[16,4] 2.174 1.267 0.075 2.542 4.687
beta1_pH[11,5] 61.284 140.617 1.489 9.554 561.599
beta1_pH[12,5] 64.295 126.645 3.472 18.192 503.635
beta1_pH[13,5] 75.325 229.232 3.374 15.697 398.442
beta1_pH[14,5] 380.800 667.703 1.538 15.801 2206.319
beta1_pH[15,5] 35.729 75.000 1.920 9.761 293.931
beta1_pH[16,5] 28.075 64.349 0.687 10.596 187.259
beta2_pH[1,1] 0.494 0.178 0.248 0.465 0.911
beta2_pH[2,1] 0.503 0.309 0.192 0.436 1.243
beta2_pH[3,1] 0.450 0.333 0.140 0.382 1.136
beta2_pH[4,1] 0.386 0.182 0.172 0.354 0.776
beta2_pH[5,1] 1.114 1.420 0.045 0.599 4.965
beta2_pH[6,1] 0.730 1.170 0.117 0.337 4.409
beta2_pH[7,1] -0.378 1.465 -4.392 0.003 1.450
beta2_pH[8,1] 0.381 0.361 0.148 0.313 0.994
beta2_pH[9,1] 0.656 0.681 0.182 0.486 2.527
beta2_pH[10,1] 0.791 0.733 0.263 0.590 2.790
beta2_pH[11,1] 0.238 0.053 0.150 0.233 0.359
beta2_pH[12,1] 1.151 0.555 0.486 1.027 2.507
beta2_pH[13,1] 0.269 0.074 0.161 0.259 0.441
beta2_pH[14,1] 0.269 0.067 0.183 0.256 0.447
beta2_pH[15,1] 0.219 0.062 0.133 0.208 0.367
beta2_pH[16,1] 0.607 0.394 0.140 0.575 1.435
beta2_pH[1,2] -1.598 4.316 -10.299 -1.730 6.815
beta2_pH[2,2] -3.123 3.406 -10.260 -2.918 4.171
beta2_pH[3,2] -3.582 3.041 -10.550 -3.079 1.827
beta2_pH[4,2] -3.567 3.174 -10.564 -3.268 2.957
beta2_pH[5,2] -1.277 4.256 -9.335 -1.452 7.523
beta2_pH[6,2] -1.948 3.975 -9.421 -2.112 6.800
beta2_pH[7,2] -1.878 4.143 -9.684 -2.177 7.265
beta2_pH[8,2] -1.592 4.461 -10.253 -2.004 8.152
beta2_pH[9,2] -1.983 4.118 -9.728 -2.253 6.882
beta2_pH[10,2] -2.381 4.140 -10.338 -2.680 6.585
beta2_pH[11,2] -6.432 2.544 -12.526 -5.934 -2.738
beta2_pH[12,2] -2.983 2.601 -9.932 -1.968 -0.539
beta2_pH[13,2] -3.653 2.260 -9.791 -2.936 -1.261
beta2_pH[14,2] -4.711 2.516 -11.138 -4.069 -1.706
beta2_pH[15,2] -6.405 2.561 -12.585 -5.879 -2.750
beta2_pH[16,2] -4.425 4.193 -12.572 -5.120 1.798
beta2_pH[1,3] 3.204 2.503 0.271 2.641 9.607
beta2_pH[2,3] -0.403 4.489 -8.101 0.267 8.141
beta2_pH[3,3] -0.826 4.229 -9.106 -1.426 7.847
beta2_pH[4,3] 0.695 4.204 -8.109 0.880 8.700
beta2_pH[5,3] 4.979 2.834 0.383 4.650 11.295
beta2_pH[6,3] 5.173 2.893 0.692 4.753 12.258
beta2_pH[7,3] 4.871 2.432 0.802 4.692 10.164
beta2_pH[8,3] 5.962 2.496 2.053 5.605 11.569
beta2_pH[9,3] 5.210 2.506 1.367 4.848 11.296
beta2_pH[10,3] 4.581 2.525 0.606 4.500 10.179
beta2_pH[11,4] -1.441 2.393 -7.975 -0.533 1.969
beta2_pH[12,4] -1.668 2.357 -7.658 -1.211 3.184
beta2_pH[13,4] 0.509 2.209 -2.454 0.719 5.057
beta2_pH[14,4] -0.133 3.895 -7.693 -0.850 9.649
beta2_pH[15,4] 1.761 1.930 -1.515 1.465 6.303
beta2_pH[16,4] 3.415 2.879 -0.203 3.173 9.662
beta2_pH[11,5] -3.070 2.305 -9.258 -2.402 -0.597
beta2_pH[12,5] -3.980 2.692 -11.041 -3.249 -0.786
beta2_pH[13,5] -1.506 3.085 -7.738 -1.805 4.511
beta2_pH[14,5] -4.081 2.609 -10.693 -3.382 -1.003
beta2_pH[15,5] -3.920 2.412 -10.107 -3.310 -0.891
beta2_pH[16,5] -3.352 2.555 -9.686 -2.734 -0.494
beta3_pH[1,1] 35.752 1.106 33.615 35.714 38.032
beta3_pH[2,1] 34.392 1.815 31.597 34.126 38.694
beta3_pH[3,1] 35.703 2.069 32.484 35.407 41.205
beta3_pH[4,1] 36.272 1.989 32.900 36.073 40.753
beta3_pH[5,1] 29.415 3.558 22.591 28.397 37.926
beta3_pH[6,1] 40.619 3.175 33.468 41.484 45.301
beta3_pH[7,1] 29.849 9.585 18.427 26.358 45.721
beta3_pH[8,1] 39.025 2.107 34.974 38.992 43.614
beta3_pH[9,1] 31.186 1.990 27.777 31.020 35.763
beta3_pH[10,1] 33.005 1.288 30.633 32.938 35.751
beta3_pH[11,1] 35.543 1.495 32.929 35.471 38.827
beta3_pH[12,1] 30.490 0.524 29.390 30.506 31.497
beta3_pH[13,1] 39.140 2.220 35.390 38.914 43.881
beta3_pH[14,1] 41.539 1.994 38.139 41.297 45.570
beta3_pH[15,1] 41.093 2.792 36.022 41.077 45.710
beta3_pH[16,1] 44.535 1.186 41.311 44.743 45.952
beta3_pH[1,2] 31.330 8.785 18.530 29.181 44.372
beta3_pH[2,2] 28.432 6.671 18.500 27.998 43.321
beta3_pH[3,2] 37.900 7.607 19.343 41.542 44.246
beta3_pH[4,2] 31.487 9.267 18.628 28.856 44.858
beta3_pH[5,2] 30.310 8.025 18.529 29.459 45.090
beta3_pH[6,2] 32.297 6.666 18.791 34.580 44.276
beta3_pH[7,2] 29.541 7.710 18.477 28.500 44.858
beta3_pH[8,2] 29.145 7.669 18.390 28.155 44.462
beta3_pH[9,2] 35.499 9.414 18.694 38.309 45.710
beta3_pH[10,2] 29.793 6.634 18.892 29.364 43.919
beta3_pH[11,2] 43.365 0.168 43.099 43.342 43.727
beta3_pH[12,2] 43.112 0.318 42.367 43.134 43.733
beta3_pH[13,2] 43.799 0.209 43.253 43.836 44.137
beta3_pH[14,2] 43.338 0.192 43.049 43.312 43.792
beta3_pH[15,2] 43.393 0.170 43.117 43.375 43.761
beta3_pH[16,2] 36.161 10.521 18.241 43.377 43.778
beta3_pH[1,3] 40.032 0.987 37.728 40.100 41.576
beta3_pH[2,3] 30.020 7.586 18.459 29.284 44.990
beta3_pH[3,3] 33.877 8.274 18.784 33.823 44.352
beta3_pH[4,3] 27.606 7.090 18.338 26.346 44.477
beta3_pH[5,3] 27.154 6.045 18.542 27.025 42.437
beta3_pH[6,3] 30.596 4.316 19.793 31.790 38.680
beta3_pH[7,3] 25.443 2.164 22.657 24.878 29.530
beta3_pH[8,3] 41.494 0.221 41.087 41.495 41.918
beta3_pH[9,3] 33.759 0.449 32.977 33.773 34.715
beta3_pH[10,3] 36.060 0.540 34.617 36.109 36.871
beta3_pH[11,4] 40.824 4.470 30.552 42.530 45.830
beta3_pH[12,4] 40.975 3.206 30.227 41.981 45.088
beta3_pH[13,4] 36.825 5.681 29.774 35.845 44.656
beta3_pH[14,4] 37.723 5.713 29.217 40.810 45.297
beta3_pH[15,4] 31.596 3.391 29.217 30.112 42.812
beta3_pH[16,4] 31.480 3.141 29.103 29.634 39.398
beta3_pH[11,5] 39.705 1.574 35.813 39.876 42.549
beta3_pH[12,5] 38.304 1.999 34.627 38.201 42.634
beta3_pH[13,5] 37.871 3.276 31.441 39.529 41.308
beta3_pH[14,5] 38.887 1.586 35.107 39.110 41.693
beta3_pH[15,5] 40.001 1.012 37.139 40.292 41.129
beta3_pH[16,5] 38.450 2.039 32.057 38.870 40.999
beta0_pelagic[1] 1.931 0.478 0.609 2.091 2.415
beta0_pelagic[2] 1.424 0.237 0.801 1.471 1.737
beta0_pelagic[3] 0.274 0.284 -0.363 0.307 0.763
beta0_pelagic[4] 0.275 0.540 -1.074 0.353 1.093
beta0_pelagic[5] 0.490 1.428 -2.979 1.245 1.679
beta0_pelagic[6] 1.561 0.224 1.118 1.585 1.855
beta0_pelagic[7] 1.526 0.146 1.234 1.528 1.787
beta0_pelagic[8] 1.854 0.152 1.552 1.863 2.136
beta0_pelagic[9] 2.072 0.711 0.343 2.285 2.858
beta0_pelagic[10] 2.517 0.256 1.674 2.564 2.815
beta0_pelagic[11] 0.647 0.195 0.218 0.663 0.942
beta0_pelagic[12] 1.757 0.133 1.496 1.758 2.020
beta0_pelagic[13] 0.551 0.155 0.248 0.553 0.853
beta0_pelagic[14] 0.391 0.193 -0.032 0.406 0.734
beta0_pelagic[15] -0.248 0.131 -0.498 -0.248 0.016
beta0_pelagic[16] 0.547 0.134 0.289 0.549 0.807
beta1_pelagic[1] 0.316 0.495 0.000 0.071 1.698
beta1_pelagic[2] 0.171 0.248 0.000 0.049 0.839
beta1_pelagic[3] 0.781 0.371 0.148 0.732 1.755
beta1_pelagic[4] 0.906 0.572 0.000 0.839 2.244
beta1_pelagic[5] 0.984 1.618 0.000 0.004 4.713
beta1_pelagic[6] 0.099 0.344 0.000 0.001 0.880
beta1_pelagic[7] 0.430 1.807 0.000 0.001 6.311
beta1_pelagic[8] 0.181 0.890 0.000 0.001 1.285
beta1_pelagic[9] 0.903 1.791 0.000 0.671 3.254
beta1_pelagic[10] 0.118 0.383 0.000 0.001 1.124
beta1_pelagic[11] 2.529 0.606 1.876 2.427 4.634
beta1_pelagic[12] 2.633 0.264 2.123 2.631 3.170
beta1_pelagic[13] 2.357 0.495 1.557 2.294 3.625
beta1_pelagic[14] 3.249 0.745 2.183 3.081 5.063
beta1_pelagic[15] 2.542 0.249 2.068 2.540 3.023
beta1_pelagic[16] 3.014 0.277 2.525 3.000 3.593
beta2_pelagic[1] 2.041 2.617 -3.678 1.728 8.351
beta2_pelagic[2] 2.125 2.626 -2.937 1.843 7.733
beta2_pelagic[3] 2.280 2.298 0.102 1.615 8.192
beta2_pelagic[4] 2.435 2.497 -0.587 1.764 8.831
beta2_pelagic[5] -0.529 4.058 -8.175 -1.190 7.958
beta2_pelagic[6] 0.418 4.047 -7.845 0.471 8.510
beta2_pelagic[7] -0.025 4.141 -8.367 0.114 8.234
beta2_pelagic[8] -0.037 4.049 -8.131 -0.199 8.154
beta2_pelagic[9] 1.316 3.672 -6.999 1.102 8.643
beta2_pelagic[10] 0.315 4.173 -8.272 0.402 8.692
beta2_pelagic[11] 3.869 2.579 0.242 3.393 10.052
beta2_pelagic[12] 5.417 2.758 1.731 4.859 12.069
beta2_pelagic[13] 1.547 1.924 0.267 0.823 7.507
beta2_pelagic[14] 0.523 0.496 0.207 0.449 1.228
beta2_pelagic[15] 4.572 2.962 0.904 3.992 11.576
beta2_pelagic[16] 5.105 2.676 0.947 4.852 11.088
beta3_pelagic[1] 27.080 7.348 18.452 24.145 44.122
beta3_pelagic[2] 29.448 8.307 18.350 28.148 44.845
beta3_pelagic[3] 29.425 4.047 22.902 29.499 39.996
beta3_pelagic[4] 25.635 4.155 19.936 25.096 39.163
beta3_pelagic[5] 34.587 9.891 18.672 34.980 45.989
beta3_pelagic[6] 30.124 7.908 18.544 29.268 44.616
beta3_pelagic[7] 29.595 8.230 18.506 28.306 44.855
beta3_pelagic[8] 29.303 7.676 18.464 27.855 44.554
beta3_pelagic[9] 29.057 6.348 18.810 27.316 43.553
beta3_pelagic[10] 28.891 7.870 18.380 27.589 44.995
beta3_pelagic[11] 43.295 0.512 42.433 43.239 44.833
beta3_pelagic[12] 43.460 0.233 43.043 43.456 43.905
beta3_pelagic[13] 42.869 1.006 40.835 42.932 45.092
beta3_pelagic[14] 43.038 1.357 40.325 43.043 45.617
beta3_pelagic[15] 43.143 0.322 42.288 43.188 43.649
beta3_pelagic[16] 43.244 0.278 42.518 43.264 43.697
mu_beta0_pelagic[1] 0.919 0.822 -0.828 0.947 2.544
mu_beta0_pelagic[2] 1.641 0.604 0.116 1.722 2.572
mu_beta0_pelagic[3] 0.606 0.414 -0.219 0.607 1.418
tau_beta0_pelagic[1] 1.304 3.060 0.065 0.650 5.316
tau_beta0_pelagic[2] 3.061 6.096 0.093 1.572 14.138
tau_beta0_pelagic[3] 1.901 1.392 0.259 1.518 5.342
beta0_yellow[1] -0.523 0.188 -0.940 -0.504 -0.226
beta0_yellow[2] 0.460 0.233 -0.102 0.489 0.779
beta0_yellow[3] -0.320 0.199 -0.737 -0.307 0.024
beta0_yellow[4] 0.731 0.357 -0.237 0.812 1.181
beta0_yellow[5] -1.240 0.415 -2.092 -1.242 -0.449
beta0_yellow[6] 0.246 0.208 -0.171 0.250 0.641
beta0_yellow[7] 0.974 0.395 -0.468 1.042 1.342
beta0_yellow[8] 0.733 0.633 -1.204 0.954 1.293
beta0_yellow[9] -0.045 0.291 -0.588 -0.056 0.552
beta0_yellow[10] 0.241 0.151 -0.062 0.239 0.536
beta0_yellow[11] -1.801 0.442 -2.688 -1.784 -0.971
beta0_yellow[12] -3.570 0.435 -4.474 -3.544 -2.770
beta0_yellow[13] -3.600 0.461 -4.580 -3.560 -2.784
beta0_yellow[14] -1.922 0.666 -2.970 -2.017 -0.234
beta0_yellow[15] -2.780 0.414 -3.645 -2.772 -2.009
beta0_yellow[16] -2.164 0.500 -3.065 -2.192 -1.036
beta1_yellow[1] 0.518 0.898 0.000 0.310 2.004
beta1_yellow[2] 1.155 0.501 0.606 1.055 2.682
beta1_yellow[3] 0.685 0.320 0.113 0.666 1.377
beta1_yellow[4] 1.711 1.039 0.704 1.331 4.741
beta1_yellow[5] 2.988 1.538 1.298 2.845 5.202
beta1_yellow[6] 2.304 0.349 1.655 2.293 3.000
beta1_yellow[7] 6.080 6.787 0.556 4.275 20.333
beta1_yellow[8] 2.357 2.254 0.026 1.914 8.250
beta1_yellow[9] 1.596 1.141 0.767 1.528 2.714
beta1_yellow[10] 2.638 0.489 1.749 2.608 3.681
beta1_yellow[11] 1.962 0.439 1.097 1.955 2.821
beta1_yellow[12] 2.356 0.442 1.571 2.328 3.293
beta1_yellow[13] 2.777 0.465 1.986 2.725 3.770
beta1_yellow[14] 2.022 0.570 0.702 2.071 3.042
beta1_yellow[15] 2.079 0.411 1.293 2.070 2.942
beta1_yellow[16] 2.007 0.475 0.981 2.026 2.879
beta2_yellow[1] -2.120 2.688 -8.489 -1.570 2.434
beta2_yellow[2] -2.488 2.368 -8.923 -1.775 -0.111
beta2_yellow[3] -2.493 2.350 -8.952 -1.798 -0.120
beta2_yellow[4] -1.504 1.992 -7.365 -0.674 -0.075
beta2_yellow[5] -4.467 2.896 -11.512 -3.922 -0.556
beta2_yellow[6] 3.599 2.254 0.967 2.999 9.375
beta2_yellow[7] -4.542 3.557 -11.879 -4.326 3.763
beta2_yellow[8] -2.221 4.066 -10.063 -2.154 6.644
beta2_yellow[9] 3.642 2.686 0.147 3.373 9.612
beta2_yellow[10] -4.717 2.640 -11.167 -4.213 -1.054
beta2_yellow[11] -4.242 2.353 -10.180 -3.710 -1.199
beta2_yellow[12] -4.620 2.576 -11.344 -3.943 -1.324
beta2_yellow[13] -4.334 2.439 -10.361 -3.776 -1.458
beta2_yellow[14] -4.271 2.402 -9.669 -3.787 -0.662
beta2_yellow[15] -3.876 2.087 -8.904 -3.418 -1.150
beta2_yellow[16] -4.403 2.395 -10.662 -3.878 -1.317
beta3_yellow[1] 27.790 7.480 18.400 25.955 44.608
beta3_yellow[2] 29.189 2.377 23.999 28.983 33.883
beta3_yellow[3] 32.977 3.164 24.777 32.951 39.843
beta3_yellow[4] 28.753 3.902 19.915 28.188 35.891
beta3_yellow[5] 33.380 1.446 30.954 33.387 35.599
beta3_yellow[6] 39.645 0.513 38.735 39.617 40.858
beta3_yellow[7] 20.748 3.045 18.647 20.101 30.092
beta3_yellow[8] 25.773 5.409 18.375 25.335 41.033
beta3_yellow[9] 37.689 2.644 35.184 37.604 43.162
beta3_yellow[10] 29.368 0.431 28.355 29.407 30.000
beta3_yellow[11] 45.332 0.521 44.075 45.445 45.974
beta3_yellow[12] 43.367 0.439 42.511 43.331 44.283
beta3_yellow[13] 44.844 0.397 43.973 44.909 45.513
beta3_yellow[14] 43.473 3.115 31.741 44.172 45.838
beta3_yellow[15] 45.282 0.507 44.218 45.335 45.976
beta3_yellow[16] 44.672 1.295 43.433 44.764 45.922
mu_beta0_yellow[1] 0.093 0.557 -1.018 0.079 1.311
mu_beta0_yellow[2] 0.132 0.479 -0.838 0.143 1.071
mu_beta0_yellow[3] -2.299 0.664 -3.317 -2.397 -0.588
tau_beta0_yellow[1] 2.169 3.782 0.095 1.270 8.411
tau_beta0_yellow[2] 1.300 1.269 0.151 0.979 4.190
tau_beta0_yellow[3] 1.324 1.716 0.090 0.857 5.258
beta0_black[1] 0.002 0.194 -0.347 -0.007 0.387
beta0_black[2] 1.861 0.165 1.503 1.875 2.126
beta0_black[3] 1.269 0.176 0.888 1.286 1.548
beta0_black[4] 2.133 0.344 1.549 2.143 2.610
beta0_black[5] 1.592 2.106 -3.120 1.673 5.975
beta0_black[6] 1.543 2.026 -2.968 1.642 5.576
beta0_black[7] 1.555 2.012 -3.019 1.646 5.620
beta0_black[8] 1.248 0.236 0.752 1.259 1.690
beta0_black[9] 2.402 0.281 1.837 2.415 2.900
beta0_black[10] 1.458 0.131 1.199 1.458 1.715
beta0_black[11] 3.421 0.183 3.036 3.437 3.731
beta0_black[12] 4.489 0.186 4.119 4.491 4.858
beta0_black[13] -0.099 0.218 -0.543 -0.094 0.320
beta0_black[14] 2.131 0.508 0.739 2.258 2.762
beta0_black[15] 1.140 0.333 0.273 1.204 1.540
beta0_black[16] 4.004 0.678 1.754 4.205 4.539
beta2_black[1] 2.335 3.556 -6.199 2.375 9.297
beta2_black[2] -0.469 4.154 -8.800 -0.615 8.742
beta2_black[3] 0.033 4.280 -8.714 0.092 8.511
beta2_black[4] -1.766 3.559 -8.984 -1.571 6.301
beta2_black[5] -0.347 4.292 -8.907 -0.287 8.054
beta2_black[6] -0.266 4.348 -9.063 -0.404 8.571
beta2_black[7] -0.292 4.118 -8.350 -0.268 7.874
beta2_black[8] -0.389 4.308 -8.842 -0.503 8.371
beta2_black[9] -0.411 4.217 -8.908 -0.470 8.226
beta2_black[10] -0.336 4.259 -8.772 -0.520 8.289
beta2_black[11] -2.510 1.758 -6.133 -2.325 0.066
beta2_black[12] -3.024 1.972 -8.042 -2.554 -0.660
beta2_black[13] -2.530 1.861 -7.549 -2.001 -0.539
beta2_black[14] -1.803 1.729 -5.996 -1.309 -0.097
beta2_black[15] -2.080 2.193 -7.261 -1.867 1.742
beta2_black[16] -1.793 2.734 -7.855 -1.766 3.671
beta3_black[1] 37.990 6.980 19.781 41.457 43.335
beta3_black[2] 29.954 7.950 18.430 29.404 44.751
beta3_black[3] 29.256 7.831 18.523 28.598 44.675
beta3_black[4] 32.139 5.439 19.416 32.679 43.110
beta3_black[5] 30.089 7.942 18.599 29.094 44.962
beta3_black[6] 29.888 7.957 18.431 28.906 44.891
beta3_black[7] 30.111 7.980 18.472 29.242 45.026
beta3_black[8] 30.090 7.942 18.571 29.151 44.674
beta3_black[9] 30.206 7.897 18.494 29.406 44.699
beta3_black[10] 29.922 7.786 18.521 28.992 44.681
beta3_black[11] 30.072 6.901 18.728 30.034 43.646
beta3_black[12] 32.821 1.045 30.745 32.943 33.871
beta3_black[13] 39.334 0.639 37.813 39.376 40.444
beta3_black[14] 38.118 3.966 26.162 38.768 44.838
beta3_black[15] 31.575 7.922 18.644 31.255 45.039
beta3_black[16] 28.374 7.412 18.408 26.931 44.763
beta4_black[1] -0.264 0.185 -0.628 -0.263 0.103
beta4_black[2] 0.250 0.174 -0.083 0.248 0.588
beta4_black[3] -0.932 0.184 -1.295 -0.932 -0.570
beta4_black[4] 0.506 0.231 0.064 0.503 0.958
beta4_black[5] 0.243 2.645 -4.458 0.164 4.766
beta4_black[6] 0.224 2.760 -4.843 0.141 5.334
beta4_black[7] 0.286 2.658 -4.482 0.145 5.544
beta4_black[8] -0.688 0.362 -1.384 -0.686 0.018
beta4_black[9] 1.466 1.002 -0.104 1.338 3.761
beta4_black[10] 0.026 0.178 -0.328 0.030 0.366
beta4_black[11] -0.693 0.203 -1.100 -0.692 -0.305
beta4_black[12] 0.290 0.324 -0.336 0.282 0.919
beta4_black[13] -1.194 0.211 -1.607 -1.194 -0.783
beta4_black[14] -0.124 0.224 -0.561 -0.122 0.305
beta4_black[15] -0.890 0.204 -1.297 -0.887 -0.500
beta4_black[16] -0.595 0.220 -1.020 -0.598 -0.159
mu_beta0_black[1] 1.221 0.872 -0.764 1.260 2.887
mu_beta0_black[2] 1.583 0.913 -0.520 1.639 3.335
mu_beta0_black[3] 2.294 0.974 0.217 2.327 4.151
tau_beta0_black[1] 0.781 0.774 0.057 0.536 2.881
tau_beta0_black[2] 2.089 4.517 0.055 0.849 10.795
tau_beta0_black[3] 0.258 0.180 0.052 0.211 0.708
beta0_dsr[11] -3.046 0.271 -3.577 -3.045 -2.506
beta0_dsr[12] 4.475 0.271 3.944 4.478 5.000
beta0_dsr[13] -1.586 0.386 -2.286 -1.557 -0.977
beta0_dsr[14] -4.157 0.484 -5.126 -4.149 -3.234
beta0_dsr[15] -2.412 0.264 -2.933 -2.401 -1.906
beta0_dsr[16] -2.958 0.365 -3.700 -2.956 -2.250
beta1_dsr[11] 4.923 0.287 4.371 4.921 5.486
beta1_dsr[12] 6.351 4.773 2.458 5.239 16.156
beta1_dsr[13] 3.061 0.437 2.467 3.012 3.930
beta1_dsr[14] 6.788 0.511 5.807 6.791 7.788
beta1_dsr[15] 3.601 0.267 3.092 3.604 4.124
beta1_dsr[16] 5.756 0.381 5.016 5.760 6.508
beta2_dsr[11] -8.262 2.340 -13.791 -7.963 -4.656
beta2_dsr[12] -7.096 2.607 -13.051 -6.892 -2.540
beta2_dsr[13] -6.335 2.783 -11.902 -6.331 -0.547
beta2_dsr[14] -6.584 2.441 -11.902 -6.360 -2.610
beta2_dsr[15] -7.635 2.462 -13.504 -7.233 -3.784
beta2_dsr[16] -7.882 2.331 -13.113 -7.573 -4.164
beta3_dsr[11] 43.484 0.148 43.210 43.481 43.761
beta3_dsr[12] 33.996 0.705 32.262 34.130 34.816
beta3_dsr[13] 43.245 0.310 42.848 43.175 43.885
beta3_dsr[14] 43.266 0.143 43.080 43.230 43.626
beta3_dsr[15] 43.469 0.182 43.147 43.462 43.823
beta3_dsr[16] 43.438 0.156 43.181 43.424 43.760
beta4_dsr[11] 0.667 0.209 0.262 0.666 1.080
beta4_dsr[12] 0.311 0.482 -0.650 0.323 1.259
beta4_dsr[13] -0.097 0.214 -0.535 -0.097 0.326
beta4_dsr[14] 0.205 0.253 -0.291 0.212 0.686
beta4_dsr[15] 0.991 0.209 0.591 0.993 1.392
beta4_dsr[16] 0.158 0.232 -0.298 0.165 0.603
beta0_slope[11] -2.004 0.158 -2.321 -2.003 -1.693
beta0_slope[12] -4.699 0.268 -5.221 -4.695 -4.185
beta0_slope[13] -1.438 0.231 -2.022 -1.412 -1.078
beta0_slope[14] -2.654 0.208 -3.049 -2.657 -2.249
beta0_slope[15] -1.711 0.157 -2.022 -1.714 -1.398
beta0_slope[16] -2.768 0.166 -3.088 -2.766 -2.446
beta1_slope[11] 4.394 0.291 3.835 4.394 4.961
beta1_slope[12] 4.851 0.527 3.807 4.842 5.907
beta1_slope[13] 2.724 0.588 1.988 2.607 4.472
beta1_slope[14] 6.052 0.850 4.664 5.963 8.040
beta1_slope[15] 2.010 0.283 1.464 2.009 2.558
beta1_slope[16] 5.298 0.388 4.555 5.297 6.081
beta2_slope[11] 7.768 2.444 3.997 7.398 13.393
beta2_slope[12] 6.039 2.746 1.571 5.694 12.328
beta2_slope[13] 4.241 2.807 0.287 3.874 10.573
beta2_slope[14] 2.562 2.405 0.728 1.456 9.286
beta2_slope[15] 6.445 2.549 2.493 6.088 12.393
beta2_slope[16] 7.106 2.400 3.414 6.771 12.647
beta3_slope[11] 43.494 0.154 43.211 43.489 43.790
beta3_slope[12] 43.355 0.247 42.945 43.328 43.856
beta3_slope[13] 43.576 0.550 42.603 43.603 44.599
beta3_slope[14] 44.672 0.421 43.818 44.695 45.370
beta3_slope[15] 43.593 0.251 43.115 43.598 44.056
beta3_slope[16] 43.467 0.168 43.185 43.456 43.799
beta4_slope[11] -0.462 0.208 -0.868 -0.463 -0.058
beta4_slope[12] -1.242 0.675 -2.722 -1.157 -0.189
beta4_slope[13] 0.170 0.211 -0.229 0.168 0.586
beta4_slope[14] -0.102 0.252 -0.617 -0.105 0.400
beta4_slope[15] -0.189 0.201 -0.579 -0.184 0.196
beta4_slope[16] -0.131 0.222 -0.549 -0.131 0.309
sigma_H[1] 0.198 0.054 0.096 0.196 0.311
sigma_H[2] 0.171 0.030 0.120 0.168 0.234
sigma_H[3] 0.197 0.043 0.120 0.194 0.288
sigma_H[4] 0.421 0.075 0.298 0.413 0.595
sigma_H[5] 0.983 0.210 0.611 0.977 1.439
sigma_H[6] 0.372 0.200 0.026 0.367 0.776
sigma_H[7] 0.300 0.058 0.206 0.293 0.436
sigma_H[8] 0.427 0.092 0.286 0.417 0.629
sigma_H[9] 0.516 0.122 0.326 0.500 0.781
sigma_H[10] 0.216 0.043 0.143 0.213 0.308
sigma_H[11] 0.277 0.046 0.200 0.273 0.377
sigma_H[12] 0.443 0.167 0.209 0.423 0.779
sigma_H[13] 0.215 0.037 0.149 0.212 0.294
sigma_H[14] 0.508 0.094 0.346 0.502 0.712
sigma_H[15] 0.249 0.040 0.181 0.245 0.336
sigma_H[16] 0.228 0.044 0.154 0.224 0.325
lambda_H[1] 3.222 4.361 0.148 1.702 15.468
lambda_H[2] 8.102 7.606 0.758 6.005 29.113
lambda_H[3] 6.211 9.346 0.273 3.082 30.884
lambda_H[4] 0.007 0.004 0.001 0.005 0.018
lambda_H[5] 3.613 7.930 0.033 0.946 26.575
lambda_H[6] 7.595 14.771 0.009 1.028 47.907
lambda_H[7] 0.014 0.009 0.002 0.011 0.038
lambda_H[8] 8.023 10.101 0.006 4.492 34.924
lambda_H[9] 0.016 0.010 0.003 0.013 0.041
lambda_H[10] 0.306 0.641 0.034 0.189 1.191
lambda_H[11] 0.239 0.350 0.012 0.127 1.014
lambda_H[12] 4.975 6.671 0.203 2.790 23.009
lambda_H[13] 3.217 2.965 0.244 2.359 11.070
lambda_H[14] 3.599 4.270 0.223 2.187 15.470
lambda_H[15] 0.025 0.031 0.003 0.017 0.101
lambda_H[16] 1.457 2.344 0.027 0.666 7.457
mu_lambda_H[1] 4.348 1.917 1.238 4.195 8.539
mu_lambda_H[2] 3.869 1.959 0.586 3.718 7.963
mu_lambda_H[3] 3.588 1.847 0.777 3.353 7.709
sigma_lambda_H[1] 8.633 4.242 2.154 8.064 18.178
sigma_lambda_H[2] 8.439 4.623 1.089 7.993 18.232
sigma_lambda_H[3] 6.409 3.976 0.936 5.556 16.085
beta_H[1,1] 6.873 1.056 4.429 7.042 8.470
beta_H[2,1] 9.869 0.489 8.821 9.906 10.752
beta_H[3,1] 7.984 0.793 6.184 8.072 9.244
beta_H[4,1] 9.482 7.596 -6.114 9.626 24.246
beta_H[5,1] 0.089 2.341 -4.865 0.292 4.090
beta_H[6,1] 3.279 3.902 -6.890 4.684 7.736
beta_H[7,1] 0.811 5.655 -11.584 1.238 10.552
beta_H[8,1] 2.118 7.018 -2.516 1.284 20.840
beta_H[9,1] 13.128 5.614 2.366 13.064 24.034
beta_H[10,1] 7.067 1.664 3.547 7.117 10.206
beta_H[11,1] 5.149 3.385 -2.630 5.852 9.784
beta_H[12,1] 2.599 1.028 0.820 2.538 4.794
beta_H[13,1] 9.051 0.904 7.116 9.123 10.592
beta_H[14,1] 2.195 1.001 0.237 2.175 4.157
beta_H[15,1] -6.040 3.917 -13.249 -6.339 2.554
beta_H[16,1] 3.795 2.879 -0.369 3.335 11.487
beta_H[1,2] 7.899 0.249 7.390 7.905 8.370
beta_H[2,2] 10.027 0.135 9.756 10.025 10.289
beta_H[3,2] 8.947 0.198 8.545 8.953 9.335
beta_H[4,2] 3.514 1.475 0.814 3.417 6.572
beta_H[5,2] 1.976 0.947 0.095 1.987 3.784
beta_H[6,2] 5.801 1.071 3.182 5.986 7.386
beta_H[7,2] 2.534 1.108 0.548 2.460 4.917
beta_H[8,2] 2.831 1.755 -2.654 3.142 4.258
beta_H[9,2] 3.402 1.089 1.312 3.393 5.525
beta_H[10,2] 8.183 0.353 7.446 8.199 8.844
beta_H[11,2] 9.728 0.603 8.807 9.618 11.068
beta_H[12,2] 3.924 0.359 3.238 3.922 4.657
beta_H[13,2] 9.115 0.254 8.664 9.104 9.616
beta_H[14,2] 4.008 0.342 3.356 3.992 4.700
beta_H[15,2] 11.351 0.709 9.858 11.388 12.672
beta_H[16,2] 4.772 0.796 3.201 4.792 6.282
beta_H[1,3] 8.487 0.241 8.056 8.469 9.003
beta_H[2,3] 10.075 0.116 9.851 10.074 10.311
beta_H[3,3] 9.620 0.163 9.309 9.615 9.951
beta_H[4,3] -2.453 0.901 -4.291 -2.424 -0.664
beta_H[5,3] 3.900 0.616 2.663 3.907 5.149
beta_H[6,3] 8.120 1.205 6.470 7.723 10.768
beta_H[7,3] -2.604 0.733 -4.072 -2.589 -1.166
beta_H[8,3] 5.332 0.774 4.658 5.191 7.836
beta_H[9,3] -2.723 0.717 -4.123 -2.728 -1.397
beta_H[10,3] 8.743 0.279 8.230 8.738 9.293
beta_H[11,3] 8.549 0.277 7.930 8.572 9.046
beta_H[12,3] 5.254 0.302 4.540 5.288 5.753
beta_H[13,3] 8.813 0.182 8.450 8.812 9.160
beta_H[14,3] 5.681 0.272 5.066 5.707 6.168
beta_H[15,3] 10.363 0.325 9.726 10.357 10.995
beta_H[16,3] 6.262 1.015 3.860 6.606 7.502
beta_H[1,4] 8.279 0.175 7.908 8.291 8.590
beta_H[2,4] 10.130 0.121 9.877 10.138 10.347
beta_H[3,4] 10.118 0.165 9.758 10.132 10.414
beta_H[4,4] 11.757 0.455 10.843 11.766 12.664
beta_H[5,4] 5.570 0.787 4.299 5.467 7.420
beta_H[6,4] 7.188 0.888 5.124 7.462 8.368
beta_H[7,4] 8.220 0.354 7.510 8.224 8.923
beta_H[8,4] 6.665 0.337 5.739 6.710 7.099
beta_H[9,4] 7.184 0.462 6.252 7.181 8.107
beta_H[10,4] 7.746 0.244 7.296 7.740 8.260
beta_H[11,4] 9.293 0.203 8.891 9.287 9.697
beta_H[12,4] 7.119 0.208 6.700 7.121 7.544
beta_H[13,4] 8.999 0.145 8.702 9.003 9.279
beta_H[14,4] 7.657 0.211 7.252 7.657 8.082
beta_H[15,4] 9.443 0.243 8.966 9.445 9.926
beta_H[16,4] 9.273 0.294 8.828 9.222 9.983
beta_H[1,5] 8.985 0.148 8.683 8.988 9.265
beta_H[2,5] 10.781 0.096 10.601 10.780 10.979
beta_H[3,5] 10.923 0.173 10.608 10.914 11.283
beta_H[4,5] 8.411 0.461 7.511 8.402 9.361
beta_H[5,5] 5.374 0.596 3.979 5.441 6.357
beta_H[6,5] 8.762 0.572 7.920 8.633 10.104
beta_H[7,5] 6.788 0.338 6.130 6.784 7.428
beta_H[8,5] 8.226 0.282 7.834 8.196 8.888
beta_H[9,5] 8.210 0.478 7.284 8.212 9.142
beta_H[10,5] 10.087 0.236 9.612 10.093 10.530
beta_H[11,5] 11.544 0.227 11.088 11.547 11.992
beta_H[12,5] 8.481 0.203 8.079 8.479 8.898
beta_H[13,5] 10.008 0.133 9.759 10.003 10.275
beta_H[14,5] 9.183 0.235 8.748 9.173 9.686
beta_H[15,5] 11.179 0.248 10.679 11.184 11.671
beta_H[16,5] 9.925 0.185 9.517 9.938 10.258
beta_H[1,6] 10.181 0.187 9.859 10.167 10.589
beta_H[2,6] 11.514 0.107 11.309 11.514 11.725
beta_H[3,6] 10.806 0.169 10.442 10.820 11.094
beta_H[4,6] 12.855 0.820 11.213 12.877 14.403
beta_H[5,6] 5.912 0.607 4.773 5.901 7.127
beta_H[6,6] 8.832 0.602 7.238 8.923 9.789
beta_H[7,6] 9.827 0.554 8.704 9.811 10.941
beta_H[8,6] 9.490 0.387 8.790 9.531 9.989
beta_H[9,6] 8.470 0.800 6.955 8.451 10.036
beta_H[10,6] 9.506 0.317 8.814 9.529 10.061
beta_H[11,6] 10.797 0.353 10.040 10.830 11.448
beta_H[12,6] 9.373 0.253 8.875 9.363 9.897
beta_H[13,6] 11.066 0.167 10.781 11.057 11.412
beta_H[14,6] 9.869 0.290 9.294 9.875 10.443
beta_H[15,6] 10.848 0.427 9.997 10.848 11.695
beta_H[16,6] 10.572 0.243 10.040 10.585 11.038
beta_H[1,7] 10.873 0.852 8.781 10.979 12.293
beta_H[2,7] 12.208 0.430 11.309 12.217 13.010
beta_H[3,7] 10.540 0.674 9.032 10.606 11.649
beta_H[4,7] 2.595 4.186 -5.567 2.531 11.178
beta_H[5,7] 6.529 1.898 3.210 6.456 10.888
beta_H[6,7] 9.438 2.208 4.675 9.486 14.566
beta_H[7,7] 10.662 2.774 4.778 10.719 15.911
beta_H[8,7] 11.085 1.574 9.356 10.926 13.877
beta_H[9,7] 4.408 4.137 -3.821 4.461 12.753
beta_H[10,7] 9.842 1.452 7.149 9.749 12.937
beta_H[11,7] 11.031 1.716 7.905 10.919 14.782
beta_H[12,7] 10.039 0.921 8.023 10.102 11.630
beta_H[13,7] 11.633 0.794 9.665 11.741 12.850
beta_H[14,7] 10.523 0.928 8.563 10.581 12.185
beta_H[15,7] 12.229 2.223 7.836 12.221 16.502
beta_H[16,7] 12.123 1.258 10.147 11.892 15.064
beta0_H[1] 9.063 13.713 -16.281 9.085 34.200
beta0_H[2] 10.734 6.892 -3.363 10.792 25.350
beta0_H[3] 10.092 9.864 -9.632 9.866 31.822
beta0_H[4] 4.710 185.256 -389.233 8.005 371.424
beta0_H[5] 4.307 26.322 -46.883 4.455 55.515
beta0_H[6] 6.507 48.365 -99.350 7.577 105.766
beta0_H[7] 2.116 130.258 -278.493 4.976 243.510
beta0_H[8] 7.612 56.093 -24.723 6.624 36.893
beta0_H[9] 2.663 116.568 -228.755 2.343 237.886
beta0_H[10] 8.061 33.647 -61.473 9.354 70.776
beta0_H[11] 10.910 49.447 -87.036 10.045 110.652
beta0_H[12] 6.686 11.263 -16.129 6.855 28.083
beta0_H[13] 10.160 10.940 -10.281 10.092 30.835
beta0_H[14] 6.770 11.896 -16.244 6.795 30.292
beta0_H[15] 9.296 105.257 -203.832 8.353 222.358
beta0_H[16] 7.807 27.798 -51.242 8.100 64.853